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Title:Rigidity of terminal simplices in persistent homology
Authors:ID Franc, Aleksandra (Author)
ID Virk, Žiga (Author)
Files:URL URL - Source URL, visit https://link.springer.com/article/10.1007/s13398-023-01473-z
 
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MD5: BA951B107E513AAEE2E68383B2703D7D
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:Given a filtration function on a finite simplicial complex, stability theorem of persistent homology states that the corresponding barcode is continuous with respect to changes in the filtration function. However, due to the discrete setting of simplicial complexes, the simplices terminating matched bars cannot change continuously for arbitrary perturbations of filtration functions. In this paper we provide a sufficient condition for rigidity of a terminal simplex, i.e., a condition on ε>0 implying that the terminal simplex of a homology class or a bar in persistent homology remains constant through ε-perturbations of filtration function. The condition for a homology class or a bar in dimension n depends only on the barcodes in dimensions n and n+1.
Keywords:persistent homology, stability theorem, terminal simplex, rigidity
Publication status:Published
Publication version:Version of Record
Publication date:01.10.2023
Year of publishing:2023
Number of pages:str. 1-16
Numbering:Vol. 117, iss. 4, article no. 141
PID:20.500.12556/DiRROS-18417 New window
UDC:515.1
ISSN on article:1578-7303
DOI:10.1007/s13398-023-01473-z New window
COBISS.SI-ID:157780483 New window
Publication date in DiRROS:15.03.2024
Views:585
Downloads:270
Metadata:XML DC-XML DC-RDF
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FRANC, Aleksandra and VIRK, Žiga, 2023, Rigidity of terminal simplices in persistent homology. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas [online]. 2023. Vol. 117, no. 4,  141, p. 1–16. [Accessed 6 April 2025]. DOI 10.1007/s13398-023-01473-z. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=18417
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Record is a part of a journal

Title:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas
Shortened title:Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.
Publisher:Springer Nature, Real Academia de Ciencias Exactas, Físicas y Naturales
ISSN:1578-7303
COBISS.SI-ID:17645351 New window

Document is financed by a project

Funder:ARIS - Slovenian Research and Innovation Agency
Funding programme:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Project number:N1-0114-2019
Name:Algebrajski odtisi geometrijskih značilnosti v homologiji
Funder:ARIS - Slovenian Research and Innovation Agency
Funding programme:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Project number:J1-4001-2022
Name:Izbrani problemi iz uporabne in računske topologije
Funder:ARIS - Slovenian Research and Innovation Agency
Funding programme:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Project number:J1-4031-2022
Name:Računalniška knjižnica za zavozlane strukture in aplikacije
Funder:ARIS - Slovenian Research and Innovation Agency
Funding programme:Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
Project number:P1-0292-2022
Name:Topologija in njena uporaba

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

Language:Slovenian
Keywords:vztrajna homologija, izrek o stabilnosti, končni simpleks, togost


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